Question

if A + B + C = 180 then sin^2A - sin^2b + sin^2 C = ?

Answer 1

=>(sina + sinb)(sina - sinb) + sin^2 c
=>4 sin(a+b /2) cos(a-b /2) sin(a-b /2) cos(a+b /2) + sin^2 c
=> now a+b = 180 -c
we then have
4 sin( 90 -c/2) cos(a-b /2) sin(a-b /2) cos(90- c/2) + sin^2 c
=>4cos(a-b /2) sin(a-b /2) cos(c/2) sin(c/2) + sin^2 c

now 2 sinx cosx = sin2x
=>sin(a-b)(sinc) +sin^2 c
=>sinc ( sin(a-b) + sinc)
=>sinc (2 sin(a+c-b /2) cos( a-(b+c))/2)
=>2sin c (sin(90-b) cos(90 + a)
=>-2sinc cosb sina

Answer 2

@shubhamsrg the answer should be 2sinA cos B sinc

Answer 3

@satellite73 help

Answer 4

@shubhamsrg do you know how to use equation editor??

Answer 5

@satellite73 plzzz help

Answer 6

= 2 sin(A+B)cos(A-B) + 2sinC cosC

=2sinC cos(A-B)+2sinC cosC

=2sinC (cos(A-b) + cos C)

=2sin C(cos(A-B) - cos(A+B) )

= 2sinC . 2sin A sin B
=4 sinA sin B sin C

Answer 7

@Rohangrr the answer should be 2sinA cos B sinc

Answer 8

sorry i thought of PI

Answer 9

@satellite73 plzzz help plzzz

Answer 10

sinc ( sin(a-b) + sinc) = sinc ( sin(a-b) + sin(180 - (a+b)) = sinc ( sin(a-b) + sin(a+b)) = 2 sin c sin a cos b